Alexander Grothendieck's work on functional analysis.

Abstract

After a short biographical sketch, the author describes some aspects of Alexander Grothendieck's contributions to functional analysis. He focuses on the following topics: tensor products, the approximation property, nuclear and integral operators, nuclear spaces, the Dunford-Pettis property, and Grothendieck's ``Résumé'' paper. An appendix lists all the functional analytic papers by Grothendieck.